I wasn't absolutely sure about "dynasty," so I looked further.
First, the New York Times Style Guide directs us to use lower case. The New York Times itself has thousands of examples of "dynasty," with most but not all with lower-case "d."
Second, the BBC site has both upper and lower case "D/dynasty."
Third – and this is the clincher, the Chicago Manual of Style* uses "dynasty" with a lower-case "d," except when it is part of a numeric title:
"Titles of works
As in English, titles of books and periodicals are italicized, and titles of articles are set in roman and enclosed in quotation marks. The first word of a romanized title is always capitalized, and proper nouns (especially in Japanese) often are.
Chen Shiqi, Mingdai guan shougongye de yanjiu [Studies on government-operated handicrafts during the Ming dynasty], . . .
Hua Linfu, "Qingdai yilai Sanxia diqu shuihan zaihai de chubu yanjiu" [A preliminary study of floods and droughts in the Three Gorges region since the Qing dynasty], Zhongguo shehui kexue . . .
.. a golden age. the Hellenistic period. imperial Rome. modern history. the romantic
period the Shang dynasty. the Victorian era. ...
... Under the Ming dynasty the postal service was administered by the Board of War
(bingbu) through a central office in Beijing (huitong guan). ...
A numerical designation of a period is lowercased unless it is considered part of a proper name. ...
the twenty-first century
the nineteen hundreds
the second millennium BCE
the Eighteenth Dynasty
the Fifth Republic"
So, the lower-case "d" is officially preferred by THE premier style guide in the US, and by the New York Times style guide.
(I must say that the capital "D" does not jar me, and I think most people wouldn't notice. But now that I have researched this, I will be using the lower-case "d": in dynasty.)
*The Chicago Manual of Style, 16th edition. The University of Chicago Press 2003